Method of measuring the magnetic resonance (=NMR) by means of spin echos

ABSTRACT

A method of NMR spectroscopy or tomography, wherein a sequence of temporarily offset radio frequency pulses is applied onto a spin ensemble, is characterized in that after a sequence of pulses with flip angles α 1  . . . α n  (with α 1  . . . α n ≧0°) and phases Φ 1  . . . Φ n  between which spins are dephased by φ 1  . . . φ n , a central refocusing pulse is applied as (n+1)th pulse, followed by a pulse sequence which is mirror-symmetrical to the central refocusing pulse, wherein the flip angles α n+2  . . . α 2n+1  and phases Φ n+2  . . . Φ 2n+1  of the pulses have, in comparison with the mirror-symmetrical pulses with α n  . . . α 1  and Φ n  . . . Φ 1 , negative sign with respect to amplitude and phase and the dephasings φ n+2  . . . φ 2n+1  which are also mirror-symmetrical to the central refocusing pulse in the sequence are equal to the respective mirror-symmetrical dephasings φ n  . . . φ 1  such that at the end of the pulse sequence, an output magnetization M A (Mx,My,Mz) of the spin ensemble is refocused with respect to the central refocusing pulse through application of rotation corresponding to the symmetrical relation  
       M   R (− Mx,My,−Mz )= Rot   y (180°)* M   A ( Mx,My,Mz ) 
     into a final magnetization M R =(−Mx,My,−Mz) (=hyperecho formation). In this fashion, even after application of refocusing pulses of any flip angles, the occurring signal losses can be cancelled and the complete signal amplitude can be regained with respect to dephasing through chemical shift, susceptibility and field inhomogeneity.

[0001] This application claims Paris Convention priority of Germanpatent application number 100 35 319.3 filed on Jul. 18, 2000, thecomplete disclosure of which is hereby incorporated by reference.

[0002] Method of measuring the magnetic resonance (=NMR) by means ofspin echos

BACKGROUND OF THE INVENTION

[0003] The invention concerns a method of NMR spectroscopy or nuclearmagnetic resonance tomography, wherein a sequence of temporally offsetradio frequency pulses is applied onto a spin ensemble, at least one ofwhich is designed as refocusing pulse.

[0004] In the following, reference is made to the accompanyingliterature list (“D” and corresponding numbers in round brackets).

[0005] A nuclear magnetic resonance signal is frequently measured bymeans of the spin echo method known from (D1). The excited magnetizationis thereby after a period te/2 submitted to a refocusing pulse and aspin echo is formed after a further time period te/2. At the time of thespin echo, effects acting on the spins, such as chemical shift,susceptibility, field inhomogeneity, are refocused such that all spinshave a coherent signal phase with respect to these effects. The signalmaximum is achieved if the flip angle of the refocusing pulse is exactly180°. In practice, such an ideal flip angle can only approximately berealized such that, in particular with methods based on formation ofmany spin echos, one obtains signal losses due to deviation of the flipangle of the refocusing pulses by 180°.

[0006] Such a deviation can occur either through technical facts or beartificially produced, e.g. in applications on human beings for keepingthe values of the radiated radio frequency energy within tolerablelimits (SAR=specific absorption rate). Literature proposed a series ofmeasures for limiting the corresponding signal losses. This includes onthe one hand the so-called Carr-Purrcell-Meiboom-Gill method (D2)wherein by an appropriate displacement of the pulse phase betweenexcitation and refocusing pulses, partial automatic compensation of therefocusing pulses is effected.

[0007] It could be shown that with such a sequence with long echotrains, high echo amplitudes could be achieved (D3) even with smallrefocusing flip angles.

[0008] When using different flip angles across the first refocusingperiods of the multi-echo train, the echo amplitude can be furtherincreased (D4)(D5).

[0009] In applications of analytical NMR spectroscopy, improvementsthrough different phase cycles such as MLEV16 or XY16 are used (D6).These serve mainly for compensating residual small errors in refocusingpulses with a flip angle of approximately 180°.

[0010] All methods known from literature include that in case ofdeviation of the flip angle of only one single refocusing pulse by 180°,signal loss occurs which can, at best, be reduced through correspondingdesign of the subsequent refocusing pulses.

[0011] In contrast thereto, it is the object of the present invention topresent a method for reversing the occurred signal losses even afterapplication of refocusing pulses of any flip angle, and reproduce thecomplete signal amplitude with respect to dephasing through chemicalshift, susceptibility and field inhomogeneity.

SUMMARY OF THE INVENTION

[0012] In accordance with the invention, this object is achieved in aeffective manner in that after a sequence of pulses with flip angles α₁. . . α_(n) (with α₁ . . . α_(n)≧0°) and phases Φ₁ . . . Φ_(n) betweenwhich spins are dephased by φ₁ . . . φ_(n), a central refocusing pulseis applied as (n+1)th pulse, followed by a pulse sequence which ismirror-symmetrical to the central refocusing pulse, wherein the flipangles α_(n+2) . . . α_(n+1) and phases Φ_(n+2) . . . Φ_(n+1) of thepulses have, in comparison with the corresponding pulses with α_(n) . .. α₁ and Φ_(n) . . . Φ₁, negative sign with respect to amplitude andphase and the dephasings φ_(n+2) . . . φ_(2n+1) which are alsomirror-symmetrical to the central refocusing pulse in the sequence areequal to the mirror-symmetrical dephasings φ_(n) . . . φ₁ such that atthe end of the pulse sequence, an output magnetization M_(A)(Mx,My,Mz)of the spin ensemble is transferred with respect to the centralrefocusing pulse through application of rotation corresponding to thesymmetrical relation

M _(R)(−Mx,My,−Mz)=Rot _(y)(180°)* M _(A)(Mx,My,Mz)

[0013] into a final magnetization M_(R)=(−Mx,My,−Mz) and therebyrefocused neglecting relaxation effects.

[0014] Refocusing, effected by the inventive pulse sequence, of theinitial magnetization M_(A) is characterized as hyper echo formation.

[0015] Method

[0016] The main idea is based on the observations of symmetry relationswith respect to vector rotation: We observe rotations of vectors whichhold:

[0017] Rotation about the z axis by an angle φ: $\begin{matrix}{{{Rot}_{z}\left( \phi_{n} \right)} = {\begin{matrix}{\cos \left( \phi_{n} \right)} & {\sin \left( \phi_{n} \right)} & 0 \\{- {\sin \left( \phi_{n} \right)}} & {\cos \left( \phi_{n} \right)} & 0 \\0 & 0 & 1\end{matrix}}} & \lbrack 1\rbrack\end{matrix}$

[0018] Rotation about the y axis by an angle α: $\begin{matrix}{{{Rot}_{y}\left( \alpha_{n} \right)} = {\begin{matrix}{\cos \left( \alpha_{n} \right)} & 0 & {- {\sin \left( \alpha_{n} \right)}} \\0 & 1 & 0 \\{\sin \left( \alpha_{n} \right)} & 0 & {\cos \left( \alpha_{n} \right)}\end{matrix}}} & \lbrack 2\rbrack\end{matrix}$

[0019] Rotation Rot_(Φ)(α) about a rotary axis which is tilted in thex-y plane about an angle Φ with respect to the y axis can be describedas:

Rot _(Φ)(α)=Rot _(z)(Φ_(n))Rot _(y)(α_(n))Rot _(z)(−Φ_(n))  [3]

[0020] Corresponding to the conventions of the matrix multiplication,calculation is effected from the right to the left.

[0021] Observation of two vectors V(x,y,z) and V*(−x,y,−v) which aredisposed symmetrically with respect to rotation about 180° about the yaxis, facilitates representation (FIGS. 1A-1C):

[0022] L1: Rotation Rot_(z)(φ) of a vector V(x,y,z) about the z axis atan angle φ produces the resulting vector V′(x′,y′,z). For a vectorV*(−x,y,−z) rotated with respect to V about the y axis by 180°, thepoint V*′(−x′,y′,−z) corresponding to V′ results from V* throughrotation by −φ (FIG. 1A).

[0023] Accordingly V can be transferred by rotation about z with aturning angle of Φ, subsequent rotation about y with a turning angle of180° and subsequent rotation about z with Φ in V*:

V*(−x,y,−z)=Rot _(z)(φ)*Rot _(y)(180°)*Rot _(z)(φ)*V(x,y,z)=Rot_(y)(180°)V(x,y,z).  [4]

[0024] L2: Rotation Rot_(y)(α) of V about the y axis by an angle αgenerates the resulting vector V′(x′,y,z′). The correspondingsymmetrical point V*′(−x′,y′,−z) also results from V* through rotationby α.

[0025] A trivial addition of the turning angle (FIG. 1B) thus obtains:V*(−x,y,−z)=Rot _(y)(α)*Rot _(y)(180°)*Rot _(y)(−α)*V(x,y,z)=Rot_(y)(180°)V(x,y,z).  [5]

[0026] From L1 and L2 together with equation [3] one obtains:

[0027] L3: Rotation Rot_(φ) (α) by an angle α, of V about an axis,tilted with respect to the y axis by Φ produces the resulting vectorV′(x′,y,z′). The corresponding symmetrical point V*′(−x′,y′,−z) resultsfrom V* through rotation Rot_(Φ) (α) about a rotational axis tilted withrespect to the y axis by −Φ. Therefore (FIG. 1C):

V*(−x,y,−z)=Rot _(Φ)(−α)*Rot _(y)(180°)*Rot _(Φ)(α)*V(x,y,z)

[0028] And with equations [3]-[5]:

V*(−x,y,−z)=Rot _(z)(Φ_(n))*Rot _(y)(−α_(n))*Rot _(z)(−Φ_(n))*Rot_(y)(180°)*Rot _(z)(−Φ_(n))*Rot _(y)(α_(n))*Rot_(z)(Φ_(n))*V(x,y,vz)=Rot _(y)(180°)V(x,y,z).  [6]

[0029] Rotation with −α about an axis −φ corresponds to rotation with αabout 180°−φ:

Rot _(Φ)(−α)=Rot _(180°−Φ)(α)  [7]

[0030] Both nomenclatures are equivalent and are used in the followingdepending on their practicability.

[0031] These initially purely mathematical symmetrical relations can beconverted into pulse sequences of NMR spectroscopy or MR tomography.Equation [4] is the basis of the spin echo experiment by Hahn, whichsays:

[0032] Dephasing Rot_(z)(φ), applied to magnetization M_(A)(−Mx,My,−Mz),defined as${M_{A}\left( {{M\quad x},{My},{Mz}} \right)} = {\begin{matrix}{M\quad x} \\{My} \\{Mz}\end{matrix}}$

[0033] and subsequent refocusing by a 180° pulse Rot_(y)(180°) andfurther phase development corresponding to Rot_(z)(φ) producesmagnetization M_(R)(−Mx,My,−Mz) which is rotationally symmetrical withrespect to M_(A).

[0034] Corresponding to equation [4] thus results:

M _(R)(−Mx,My,−Mz)=Rot _(z)(φ)*Rot _(y)(180°)*Rot _(z)(φ)*M_(A)(−Mx,My,−Mz)=Rot _(y)(180°)*M _(A)(Mx,My,Mz)  [8]

[0035] which means that spins are refocused by a 180° pulse independentof their phase development φ.

[0036] The phase development about φ can thereby be effected eitherthrough temporally constant mechanisms such as chemical shift,inhomogeneities etc., wherein dephasing is then characterized by an offresonance frequency ω and φ becomes proportional to the respective timeintervals corresponding to φ=ω. φ may also be determined throughvariables such as magnetic field gradients or movement in inhomogeneousfields. In terms of NMR, the rotation about a rotational axis in the x-yplane described in equations [5]-[7] corresponds to application of aradio frequency pulse with flip angle α.

[0037] Starting from the spin echo sequence corresponding to [8] samecan be symmetrically extended according to L1-L3, equations [4]-[7]thereby maintaining the rotational symmetry, wherein the sequence inboth cases is extended either by one dephasing interval corresponding toequation [4] or a pulse corresponding to equations [5]-[7].

[0038] Usually pulse sequences in MR are represented as alternatingsequence of pulses and subsequent time intervals which is also theconvention followed in the following examples of implementation. Allstatements are, of course, also true for sequences, wherein severalradio frequency pulses directly follow one another or contain severaldephasing steps between 2 radio frequency pulses.

[0039] The temporal development between two pulses may be arbitrary.Decisive is merely the total dephasing between subsequent pulses.Therefore, the inventive method can be formulated as follows:

[0040] Multiple pulse sequence in NMR spectroscopy or MR tomography,wherein a sequence of 2n+1 radio frequency pulses is applied to a spinsystem with magnetization M_(A)(Mx,My,Mz) is characterized in that atfirst n radio frequency pulses R(α_(n), Φ_(n)) are applied withrespective temporal separation t_(n) which effect rotationRot_(Φn)(α_(n)) of the spins, wherein the spins experience, in the timeintervals I_(n) between the pulses, a phase development about φ_(n)corresponding to a rotation Rot_(z)(φ_(n)) about z, and subsequently arefocusing pulse R(α_(n+1), Φ_(n+1))=R(180°, 0°) followed by n radiofrequency pulses R(α_(n+2), Φ_(n+2)) . . . R(α_(n2+1), Φ_(2n+1)) in atemporally reversed order and corresponding to the relation given inequations [5]-[7]

R(α_(n+2),Φ_(n+2)) . . . R(α_(2n+1),Φ_(2n+1))=R(−α_(n),−Φ_(n)) . . .R(−α₁,−Φ₁)=R(α_(n),180°−Φ_(n)) . . . R(α₁,180°−Φ₁)  [10]

[0041] and

φ_(n−1) . . . φ_(2n)=φ_(n) . . . φ₁  [10]

[0042] thereby obtaining magnetization M_(R) which holds:

M _(R)(−Mx,My,−Mz)=Rot _(y)(180°)*M _(A)(Mx,My,Mz),  [11]

[0043] which means that the initial magnetization M_(A) is refocusedindependently of α_(n), Φ_(n) and φ_(n).

[0044] This sequence is illustrated in FIG. 2.

[0045] According to the basic principle, that radio frequency pulseshaving a complicated amplitude and phase profile (as used e.g. for sliceselection in NMR tomography) can be represented as a sequence of shortpulses with discrete flip angle, equations [9]-[11] are validanalogously also for pulse sequences with amplitude and/orphase-modulated pulses. Additionally, it should be noted that the phaseof the central refocusing pulse was defined to be 0° and does notnecessarily need to correspond to the reference phase of magnetization.Coordination transformation of equations [9]-[11] corresponding toequation [3] makes the refocusing relation of equation [11] also validfor any phases of the central pulse if corresponding transformation iscarried out also for the other pulses.

[0046] For a central pulse having a phase ξ which effects rotationcorresponding to (180°,ξ) equation [9] results in:

R(α_(n+2),Φ_(n+2)) . . . R(α_(2n+1),Φ_(2n+1))=R(−α_(n),−Φ_(n)+2ξ) . . .R(−α₁,−Φ₁+2ξ)=R(α_(n),180°−Φ_(n)+2ξ) . . . R(α₁,180°−Φ₁+2ξ)  [12]

[0047] For completion it should be noted that the central refocusingpulse may also have a flip angle of <180°. The amplitude of the formedrefocused magnetization is then correspondingly weakened.

[0048] Such a pulse sequence refocuses all spins independent of theirrespective and optionally different phase development and form acoherent spin echo. This refocusing process through a pulse sequence iscalled below hyper-echo formation.

[0049] Relaxation proceedings were not taken into consideration in thisderivation which lead to relaxation-based signal attenuation.

[0050] It is possible to derive a series of realizations on the basis ofknown pulse sequences from the basic sequence shown in FIG. 2A.Introduction of a hyper-echo formation into an existing sequence canthereby be effected in different ways:

[0051] As shown in FIG. 2B, an existing sequence (in the present case asimple spin echo sequence having a 90° excitation pulse and a 180°refocusing pulse) can be modified through introduction of further pulsescorresponding to equations [9]-[11] into a hyper-echo sequence.Sequences where the temporal sequence of pulses already meets thedephasing conditions for hyper-echo formation thereby require optionallyonly modification of the flip angle and pulse phases (see below).

[0052]FIG. 2C shows the principle of integration of the hyper-echoformation through supplementation: Any pulse sequence (in this caseconsisting of an excitation pulse with subsequent n radio frequencypulses) is converted to a hyperecho sequence by adding a refocusingpulse and subsequent pulses according to equations [9]-[11] to form ahyper-echo.

[0053] Finally, FIG. 2D shows application of a hyper-echo for preparingmagnetization as hyper-echo which is subsequently read with any pulsesequence (in the present case a simple spin echo).

[0054] Of course, these different types of introduction of a hyper-echocan be arbitrarily combined. Formation of several hyper-echos within onesequence can also be advantageous.

[0055] Some examples of application are shown below. It must be statedthat the NMR literature describes an extremely large number of differentmultiple pulse sequences which can only be exemplarily described below.The expert can easily apply the method of symmetrization described inequations [9]-[11] for forming a completely refocused spin echo suchthat the following examples do not represent a limitation but merelyshow the general application possibilities of the basic principle.

[0056] The following application classes seem to be advantageous:

[0057] 1. Multi-echo sequences

[0058] Application of the principle described in equation [11] totransverse magnetization recovers complete magnetization—when relaxationeffects are neglected—(corresponding to the continuous use of refocusingpulses having a flip angle of 180°) for any values of α₁ . . . α_(n).While the amplitude is <<1 after each echo produced by α_(n), thecomplete amplitude is recovered after the inventive sequence.

[0059] A special case of equations [9]-[11] is given when themagnetization vector M_(A) is oriented parallel to the centralrefocusing pulse R(180°,0). In this case M_(R)=M_(A), i.e. magnetizationis converted into itself (except for relaxation effects during thesequence). This is the case e.g. in the CPMG multi echo methods (D2)wherein magnetization is generated by a 90° pulse. In the subsequentmultiple refocusing, 180° pulses are applied with a phase which isperpendicular to the excitation pulse and thus parallel to the excitedmagnetization.

[0060] Clinical application of such sequences often requires selectionof the flip angle of the refocusing pulse <180° to limit the radiofrequency output (D3). Modification of a CPMG method according to theinventive method can be realized as below:

[0061] If M_(A) is magnetization directly after excitation and possiblephase effects during the excitation pulse are neglected, the conditionM_(A) parallel to R(180°,0) is met for all subsequent refocusing pulses.For all Φ_(n) thus holds:

Φ_(n)=Φ₀=0.

[0062] Due to the equidistant refocusing pulses in CPMG sequences (andwhen using symmetrical conditions corresponding to magnetic fieldgradients for dephasing caused thereby) it is furthermore true for allφ_(n):

φ_(n)=φ₁

[0063] The symmetry of the inventive sequence is achieved in this casethrough inversion of the respectively applied flip angles. The phasesalways remain zero (FIG. 3):

R(α_(n+2),0) . . . R(α_(2n+1),0)=R(−α_(n),0) . . . R(−α₁,0)  [13]

[0064] With this modification, the amplitude of the (2n+1)th echo can bereproduced to the completely refocused value (=1) for any α₁. . . α_(n).When using such a sequence in MR tomography corresponding to the RAREmethod, the contrast of the image is essentially given by the intensityof the echo which represents the center of the k space in the phaseencoding direction.

[0065] In a preferred implementation of the inventive method, it istherefore reasonable to recover complete refocusing for exactly thisecho. Towards this end, in a first approximation, the signal intensityof the image becomes independent of a₁ . . . α_(n). Selection of α₁ . .. n_(n)<180° only slightly changes the sharpness of the image. It isadvisable thereby to chose values for α₁ . . . α_(n) which generate apossibly high and homogeneous echo amplitude as described e.g. in (D4)and (D5).

[0066] In particular, for so-called multi-contrast methods wherein phaseencoding is carried out such that at least the center of the k space isread several times and at different echo times, the principle accordingto equation [12] can be repeated several times even during an echo trainsuch that several hyper-echos can be formed in one echo train.

[0067] The chosen example of application to a RARE sequence merely hasillustrative character. Hyper-echos can be integrated also in otherimaging sequences such as GRASE, BURST etc. to improve the signalbehavior through refocusing of magnetization.

[0068] 2. Driven Equilibrium sequences

[0069] A further particularly preferred application of the inventivemethod deals with recovery of z magnetization in so-called drivenequilibrium (DEFT) sequences. Application of DEFT to spin echo sequencesfor MR imaging was described already in 1984 (D7). It is based on theapplication of a so-called flip back pulse at the time of echoformation, i.e. when all transverse magnetization is refocused. Thisflip back pulse converts the remaining transverse magnetization into zmagnetization. Same is thus closer to the thermal equilibrium whichachieves higher signal intensity with identical recovering time.

[0070] In a hyper-echo sequence, such conversion of the spin system inthe direction of balanced magnetization can be realized in two ways: Ifthe entire sequence is designed according to the principles ofhyper-echo formation and applied to z magnetization, magnetization atthe time of hyper-echo formation according to [11] will be zmagnetization. Same can be converted into z magnetization through adirectly following 180° pulse (FIG. 4A). The same effect can be achievedif the 90° pulse is phase-inverted at the end of the hyper-echo sequencethereby acting as a flip back pulse which converts magnetizationdirectly into +z magnetization (FIG. 4B).

[0071] RARE (TSE . . .) sequences having small refocusing flip angles(see above) permit rotation back to the z axis only of part of themagnetization by means of a flip back pulse due to incompleterefocusing. Application of the inventive method, however, allowsregaining of the entire transverse magnetization through formation of ahyper-echo for the time of the flip back pulse and conversion into zmagnetization through flip back.

[0072] This application is mainly (but not exclusively) useful forapplication in high field systems wherein on the one hand, often smallrefocusing flip angles are used due to the increased radio frequencyabsorption, and furthermore long repeating times are required due to thegenerally longer T1 relaxation times with increasing field strengthwithout flip back to balance out magnetization as well as possiblebefore the next excitation.

[0073] The method is thereby particularly preferred for applicationswhich offer an inherently short repeating time, such as e.g. recordingswith three-dimensional local encoding or rapidly repeated recordings forobserving temporally changing processes.

[0074] It is also possible to refocus gradient echo sequences throughhyper-echo formation by introducing a 180° pulse into the sequence afterreading out m excitation intervals, in which one gradient echo isgenerated in each case, followed by further m excitation intervals withpulses corresponding to equation [11]. FIG. 5A shows a hyper-echosequence based on a gradient echo sequence. Therein, the temporalsuccession of the entire sequence was converted after the 180° pulse andthe pulses were changed corresponding to [9]-[11]. To simplify matters,FIG. 5A shows a sequence with constant flip angle α. Taking intoconsideration equations [9]-[11] hyper-echo formation is effected alsofor sequences with variable α.

[0075] As shown, the signals recorded in the second half of the sequencecorrespond to the signal parts refocused by the 180° pulse. Since thesymmetry condition for the hyper-echo formation holds true merely forthe entire spin dephasing between two subsequent radio frequency pulsesin each case, the sequence shown in FIG. 5B also leads to hyper-echoformation. In contrast to FIG. 5A, in this case, merely the readgradient GR was temporally inverted (and the slice selection gradient GSwas made symmetrical) such that now, the gradient echos directlygenerated by the respectively preceding radio frequency pulse, wereformed also in the second half of the sequence. Considering [9]-[11]with respect to total dephasing between the pulses, a hyper-echo is alsoformed in this case.

[0076] Suitable selection of the gradients allows reading out of bothpossible signal groups (FIG. 5C). Same may either be generated and readseparately. When the reading gradient GR is designed such that theentire surface below GR between 2 refocusing pulses becomes zero, thesesignals overlap to form one single signal corresponding to the principleof the FISP sequence.

[0077] The measuring methods shown in FIGS. 5A-C can be carried outeither such that the signals used for imaging are recorded in one singlehyper-echo train. This can be carried out also such that a data setrequired for image construction is achieved only after multiplerepetition of the corresponding sequences. In particularly preferredimplementations, inversion of the initial z magnetization caused byhyper-echo formation—as already shown in the multi-echo method in FIG.4—is inverted before the recovering time tr through a 180° pulse andthus brought closer to an equilibrium (FIG. 5D).

[0078] It should finally be noted that formation of several hyper-echosis possible also for gradient echo sequences (FIG. 5E).

[0079] When the excitation pulse is started with a flip angle ofgenerally, but not necessarily 90°, the hyper-echo can also be formed assignal with transverse magnetization (FIG. 5F) which can again beconverted into z magnetization corresponding to the description formulti-echo sequences through a flip back pulse (FIG. 5G) before therecovering time tr. In the variants shown in FIGS. 5D-G, the genericsequence (FIG. 5A) was taken as a basis but also the variantscorresponding to FIGS. 5B,C (inclusive FISP) can be used.

[0080] To optimize steady-state magnetization in continuous methods suchas FIG. 5E, it may also be useful to realize the initial excitationpulse and the refocusing pulse used for hyper-echo formation not aspulses having a flip angle of 90° and 180° but as pulses withcorrespondingly smaller flip angles β (excitation) or 2β (refocusing),wherein the phase of the refocusing pulses alternates with repeatedapplication according to the principle of a true FISP sequence.

[0081] Hyper-echos can be integrated also in other imaging sequences,such as echo planar imaging, spiral imaging etc. to modify the contrastbehavior e.g. corresponding to the formation of the driven equilibrium.

[0082] The application, as described, onto measuring methods in MRimaging are merely illustrative. A large number of measuring sequencesin analytical NMR—mainly multiple-dimensional Fourier spectroscopy—suchas COSY, NOESY, INEPT, INADEQUATE etc.—to name only some of the currentsequences, is based on a plurality of repetitions of multi-pulsesequences. With all these sequences, balanced magnetization can beachieved more rapidly through formation of a hyper-echo with subsequentflip back pulse and thus reduction of the measuring time and/or increaseof the signal-to-noise ratio. If in such sequences, pulses are appliedto different nuclei, formation of hyper-echos onto all nuclei concernedis advantageous.

[0083] The use of hyper-echos in driven equilibrium sequences isparticularly advantageous mainly for observing nuclei with long T1 sincein this case, magnetization with a suitable sequence (e.g. imaging) canbe read and subsequently re-stored as z magnetization to be read outagain at a later time.

[0084] A preferred application in this case is the measurement usinghyper-polarized magnetization (e.g. through corresponding preparation ofhyper-polarized inert gases). Therein, the longitudinal magnetization isprepared in a state far beyond from the thermal equilibrium. Theprepared spin system thus produces a signal intensity which is infactors of several thousand above that of the balanced magnetization.Such hyper-polarized substances are applied e.g. in MR tomography usinghyper-polarized helium for illustrating the lung. A problem produced inthis connection is that magnetization, once it has been excited, relaxesinto the balanced state and thus loses polarization. The use of flipback sequences allows regaining of the polarized magnetization withoutthe relaxation losses caused by T2 and can thus be re-used severaltimes.

[0085] 3. Spin selection

[0086] Hyper-echo sequences may be used for selecting a sub-amount ofthe originally excited spins if modification is carried out such thatthe symmetrical condition of equation [11] leading to hyper-echoformation is fulfilled only for part of the spin. A large number of suchapplications can be derived from the plurality of sequences known in NMRliterature which can be described only illustratively and not completelybelow.

[0087] 3.1. Spin selection through variation of symmetrical conditionsfor hyper-echo formation

[0088] Spin selection in a hyper-echo experiment can be realized byselecting the pulse sequence such that the symmetrical conditions ofequation [11] are met only for part of the initially excited spins. Thiscan be achieved e.g. with application of slice-selective pulses in thatthe individual pulses act in each case only onto spins within a certainfrequency range through selection of corresponding pulse profiles. Withcorresponding selection of the respective frequency ranges, it ispossible to filter out signals from a partial range of the excitationprofile of each pulse. With simultaneous application of magnetic fieldgradients during the pulses, one can observe spins from correspondingspatial volumes.

[0089]FIG. 6 shows in this connection a simple example of application,wherein the profiles of the corresponding pulses which are symmetricalwith respect to the central 180° pulse are displaced with respect to oneanother such that hyper-echo formation is effected only in theoverlapping central spectral range (grey) whereas the signals of theouter regions appear to be dephased depending on phase and flip angle ofthe pulses.

[0090] A particularly effective type of this hyper-echo formationresults when the phase of the pulses 1 . . . n is continuouslyalternated since spins in the outer regions are submitted only to thepulses with the identical phase used in a Carr-Purrcel sequence which isknown to produce a rapid signal loss and thus signal suppression forα<180°.

[0091] Other implementations are also possible which have the commonfeature that the condition for hyper-echo formation is fulfilled only inthe region of the desired excitation window. A particularly simpleimplementation can be achieved also in that merely the centralrefocusing pulse has a different selectivity (e.g. chemical shiftselectivity) with respect to the other pulses of the hyper-echosequence.

[0092] A generalization of this principle is schematically shown in FIG.7, which shows that a complex excitation window can be obtained throughapplication of a pulse sequence with simple excitation profiles.

[0093] Spin selection is also possible through modification of thetemporal order of the pulse sequence before and/or after the central180° pulse through an additional modulation step E(φ_(E)). In case ofintroduction before the central 180° pulse, the effect of the pulsesequence is then according to equations [9]-[11] described as

M _(R)(Mx,My,Mz)=R(α₁,180°−Φ₁,φ₁) . . .*R(α_(n−1),180°−Φ_(n−1),φ_(n−1))*R(α_(n),180°−Φ_(n),φ_(n))*R(180°,0,0)*E(φ_(E))*R(α_(n),Φ_(n),φ_(n)). . . *R(α₂,Φ₂,φ₂)*R(α₁,Φ₁,φ₁)M _(A)(Mx,My,Mz)  [14]

[0094] Hyper-echo formation occurs only for that part of the spins forwhich magnetization remains unchanged, corresponding to the vectorialdisintegration, this is M_(R)COS(φ_(E)). The corresponding orthogonalcomponent M′_(R“)sees” pulses which are phase-shifted by 90° after theinterval E(φ_(E)) and therefore develops:

M′_(R)(Mx,My,Mz)=R(α₁,90°−Φ₁,φ₁)*R(α_(n−1),90°−Φ_(n−1),φ_(n−1))*R(α_(n),90°−Φ_(n),φ_(n))*R(180°,90°,0)*E(φ_(E))*R(α_(n),Φ_(n),φ_(n)). . . *R(α₂,Φ₂,φ₂)*R(α₁,Φ₁,φ₁)M _(A)(Mx,My,Mz)  [15]

[0095] With corresponding selection of Φ₁ . . . Φ_(n), this signalportion is suppressed. In the most simple case, this can be achieved forΦ₁ . . . Φ_(n)=0° and α₁ . . . α_(n)<180°.

[0096] If E is represented as an additional time interval t_(d) (FIG.8A) the symmetry of the hyper-echo sequence for resonant spins is notdisturbed. Spins having a certain off-resonance frequency ω>0 experiencein contrast thereto a phase change Δφ corresponding to Δφ=ωt_(d). Samecauses distortion of the symmetry of the hyper-echo sequence and thesignals of said spins are suppressed. E(φ_(E)) may also be designed muchmore complex.

[0097]FIG. 8B shows as further example introduction of an additionalspin echo interval with symmetrical strong magnetic field gradients.Moving spins are dephased by these gradients. When all spins moveuniformly as in vascular flow, this leads to velocity-dependent phasechanges of the observable magnetization which impairs the symmetrycondition of hyper-echo formation and thus causes attenuation of thehyper-echo signal.

[0098] Spin ensembles which move incoherently due to molecular diffusionexperience an amplitude change due to the incoherent dephasing, whichdepends on the diffusion constant and will also attenuate the amplitudeof the subsequent hyper-echo. Formation of the hyper-echo per se willnot be influenced by diffusion.

[0099] In a conventional spin echo sequence, spins moving at a constantvelocity are represented without signal loss but with altered signalphase. In a hyper-echo sequence, in which the signal portionM′_(R)(Mx,My,Mz) represented in equation [14] is dephased and thereforedoes not contribute to the total signal, phase effects do not occur.

[0100] Change of the signal phase depending on the motion and thus lossof the hyper-echo formation will occur merely through switching abipolar magnetic field gradient by one (or several) of the refocusingpulses with otherwise constant time scheme (FIG. 8C).

[0101] The embodiments shown in FIGS. 8A through 8C of a modifiedhyper-echo sequence are again exemplarily. Literature (see e.g. (D9),(D10)) shows a large number of method steps which include concretechange of the signal phase and/or amplitude and can be applied also in ahyper-echo sequence.

[0102] It is to be noted that all modifications which, when applied toconventional spin echo or gradient echo sequences, lead to phase change,effect a signal intensity loss in the hyper-echo formation. Phaseeffects will depend on the fate of the magnetization componentorthogonal to that leading to hyperecho-formation.

[0103] 3.2 Hyper-echos for suppressing of signals of coupled spins

[0104] As initially mentioned, hyper-echo refocusing according toequation [11] is true for mechanisms, such as chemical shift,susceptibility etc., i.e. spin states which are characterized by atemporal development of the phase and which are inverted by a 180°pulse. Other mechanisms such as zero and multiple-quantum coherences andJ-coupling show a different refocusing behavior and thus do not followthe same conditions for hyper-echo formation.

[0105] On the other hand, following the general symmetry relationsdescribed in Eq.[1]-[5] can also be applied to such mechanisms, suchthat a hyper-echo is then selectively formed for coupled systems,however, not for uncoupled spins. Corresponding selection of α_(n),Φ_(n), φ_(n), permits discrimination of the corresponding spin states.

[0106] Some typical applications for coupled spins are exemplarily shownbelow. This representation, too, is only exemplarily and not complete.Further applications for other states such as zero and multiple quantumcoherences can be easily derived from the basic equation [11].

[0107] Spin systems comprising J-coupling have a different refocusingbehavior than coupled spin systems which is shown by an AX system below.Extension to other systems is easily possible. An AX system ischaracterized as weakly coupled system wherein the difference of thechemical shifts of the A and X nuclei is larger than the couplingconstant J. Such a system is characterized by two doublets. If arefocusing pulse is applied to such a system, magnetizations arerefocused on the one hand and on the other hand, the correspondingcoupling partners are simultaneously exchanged which means that afterthis double inversion, the spin system behaves with respect toJ-coupling as if no refocusing had taken place.

[0108] When refocusing pulses having a flip angle of exactly 180° areapplied, this causes that the phase of the echos of coupled spinsdevelops differently than that of uncoupled spins. This is the basis ofmethods such as COSY etc.

[0109] When several pulses are applied which have a flip angle otherthan 180°, this phase development causes increasingly destructiveinterference and thus signal loss. In particular, with CPMG sequences,there is a positive interference loss of the different signalcontributions corresponding to ref. (D3) if the pulse separation withrespect to J and Δσ is sufficiently large (D8). It is therefore possibleto suppress the signals of coupled spins through a correspondingmulti-pulse sequence. Although the principle is known, such a method isnot often used in practice since the required condition of using flipangles <180° leads to signal loss of the observed uncoupled spins andthis method is disadvantageous compared to other discrimination methods.

[0110] In contrast thereto, a sequence which forms a hyper-echo withrespect to the signals of uncoupled spins results in full signalintensity, whereas signals of coupled spins are suppressed since theyeffectively _(“)see” another phase of the refocusing pulses. Towardsthis end, we observe such a doublet signal and assume that the referencefrequency is in the center of the doublet. The doublet signal will thenexperience a phase development according to cos(J/2*tn) wherein tn isthe time after excitation (FIG. 9).

[0111] A particularly advantageous feature of this application is givenin that with corresponding selection of α_(n), Φ_(n), φ_(n) signals ofspins of systems having different coupling constants can besimultaneously suppressed.

[0112] Suppression of the signals of coupled spins is prevented byselecting the time of the central 180° pulse=1/J (FIG. 9 below). This istrue, of course, only for spins having particular coupling constants J.

[0113] This principle of different phase development can be also usedfor the reversed purpose of specifically selecting coupled spins. Thisis achieved in that the phase development according to J-coupling in thephases φ_(n) of the refocusing pulses is taken into consideration.Modification of a hyper-echo sequence according to equation [11] leadsto incrementation of each pulse phase Φ_(n) about arcsin(J/2*t_(n)) andshows that formation of a hyper-echo can be achieved only for thecorresponding signal whereas for signals with different couplingconstants and also for signals with uncoupled spins, the symmetryrelation according to equation [11] is not met and same thus appearattenuated, wherein already a few refocusing pulses achieve attenuationleading to a practically complete suppression of said signals.

[0114] Corresponding to this simple example, a large number of pulsesequences can be devised which have the same feature, i.e. that thesymmetrical relation for hyper-echo formation is met in each case onlyfor the spins to be observed, however not for others. This is true inparticular also for zero and multiple-quantum coherences for which ahyper-echo method with corresponding selection or suppression of thedifferently associated signals can be easily derived from thedescription with respect to J-coupling.

[0115] The observation that when the symmetry of the phase developmentaccording to the above chapter 3 is not fulfilled, only the cosinecontribution of the magnetization contributes to the hyper-echoformation, there is the possibility of using the hyper-echo formation aspolarization filter which allows passage only of signals with a symmetryfollowing the hyper-echo sequence and deletes the signal contributionswhich are orthogonal thereto. Application of several such polarizations,optionally with selection under different polarization angles, permitsspecific selection of signals whose dephasing follows corresponding andprecise handicaps.

[0116] 4. Spin inversion

[0117] Application of a sequence according to equation [11] to pure zmagnetization leads to spin inversion as used for so-called inversionrecovery sequences for T1 measurements or also in the field of imagingfor achieving T1 weighted images. Application of a hyper-echo sequencein contrast to conventional inversion with one single 180° pulse therebypermits use of methods for selective spin inversion described underchapter 3. On the one hand, one can obtain complex inversion profiles,on the other hand, selective inversion corresponding to chemical shift,J-coupling, different zero and multiple-quantum coherences etc. ispossible.

[0118] Considerations for Implementation

[0119] In implementing hyper-echoes, one has to differentiate thatformation of hyper-echos can be integrated either in the course of themeasurement with a certain pulse sequence which is advantageous mainlyfor the sequences mentioned above in chapters 1 and 2. Implementation isalso possible or even advantageous, wherein formation of a hyper-echoinitially serves for special preparation of the spin system, and dataacquisition is carried out subsequently using any appropriate sequence(according to FIG. 2D).

[0120] The acquisition module can thereby be formed from any appropriatesignal generation sequence. Mainly in applications in MR tomography, theacquisition module may consist of a corresponding imaging module(gradient echo, echo planar imaging, RARE(TSE, . . .) spiral scan etc.)such that images are produced which have a contrast which corresponds tothe characteristic of the hyper-echo.

[0121] There are further applications wherein hyper-echos are used in adifferent context than up to now. Literature discloses (D3) that inmulti-pulse sequences, a number of possible refocusing paths fortransverse magnetization, which increases with the 3^(rd) power of thenumber of pulses, is generated of which often only part is used tocontribute to signal read-out. When such a sequence is repeated with arepetition time which is smaller than the longitudinal relaxation timeT1, undesired signals may be formed which can be prevented throughhyper-echo formation since thereby all refocusing paths are combinedagain. Such a _(“)clean-up” function may be reasonable in particularalso when using NMR in quantum computing since hyper-echo formation canserve here as deleting function of the information stored in the spinsystem as transverse magnetization.

[0122] Further advantages of the invention can be extracted from thedescription and the drawing. The features mentioned above and below maybe used in accordance with the invention either individually orcollectively in any arbitrary combination. The embodiments shown anddescribed are not to be understood as exhaustive enumeration but ratherhave exemplary character for describing the invention.

[0123] The invention is shown in the drawing and is further explained bymeans of embodiments.

BRIEF DESCRIPTION OF THE DRAWING

[0124]FIG. 1A through 1C show a demonstration of the symmetry relationswith respect to rotation;

[0125]FIG. 2A shows a hyper-echo sequence;

[0126]FIG. 2B shows the principle of application of a hyper-echosequence through integration into a known sequence;

[0127]FIG. 2C shows the principle of application of a hyper-echosequence through supplementation;

[0128]FIG. 2D shows the principle of application of a hyper-echosequence as preparation sequence;

[0129]FIG. 3 shows a pulse sequence of a modified CPMG sequencecorresponding to the inventive method;

[0130]FIG. 4 shows the principle of application of the hyper-echomechanism;

[0131]FIGS. 5A through 5G show the hyper-echo sequences on the basis ofgradient echo sequences;

[0132]FIG. 6 shows a schematic representation of the principle of spinselection;

[0133]FIG. 7 shows a generalized scheme of the principle of FIG. 6 fordemonstration how a complex excitation window can be realized from ahyper-echo sequence with pulses with shifted excitation profile;

[0134]FIGS. 8A through 8C show modified hyper-echo sequences;

[0135]FIG. 9 shows the effect of J-coupling on the hyper-echo formation;and

[0136]FIG. 10 shows a generalized scheme of a measuring sequence withhyper-echo preparation module and subsequent acquisition module.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0137]FIG. 1A shows the symmetry with respect to rotation about the zaxis corresponding to equations [4] and [8] i.e. perpendicular to theimage plane, from which follows that the vector V* obtained from Vthrough rotation about z with φ, subsequent rotation about y by 180° andsubsequent renewed rotation about z with φ (arrows) is identical to arotation of V about y by 180° (arrow shown in broken lines). The y axiswhich is perpendicular to the image plane marks the zero point of thex-z plane.

[0138]FIG. 1B shows the symmetry with respect to rotation about the yaxis corresponding to equation [5] wherein trivially a sequence ofrotations about y with α 180° and −α is identical to rotation about180°.

[0139]FIG. 1C shows the symmetry with respect to rotation about arotational axis tilted with respect to the y axis by Φ corresponding toequation [6]. Corresponding to the representation in top view, the poleof the rotational axis is shifted with respect to the zero point definedby the y axis about sin(Φ).

[0140] The radio frequency pulses with a flip angle (α₁ . . . α_(n) andthe respective phase Φ₁ . . . Φ_(n) are separated from the dephasingintervals be φ₁ . . . φ_(n) in FIG. 2A. After a central refocusingpulse, the sequence is applied in reversed order with pulses of oppositephase and amplitude. The order of the dephasing intervals is alsoreversed, however, the dephasings φ₁ . . . φ_(n) remain identical.Independent of the type of magnetization at the start of the sequence,same is refocused through the pulse sequence about the rotational axisof the refocusing pulse.

[0141] In FIG. 2B, additional pulses corresponding to the basicprinciple of FIG. 2A are introduced into an existing sequence (in thiscase: a simple spin echo experiment with a 90° and a 180° pulse (broadlines)) such that a hyper-echo is formed instead of a normal spin echo.

[0142] In FIG. 2C, an existing sequence (in this case a multi-echoexperiment with n refocusing pulses) is supplemented by a 180° pulse andthe reversed pulse sequence to form a hyper-echo. The initial excitationpulse (most often a 90° pulse) is usually not included in thesupplementation such that the hyper-echo is generated as signal oftransverse magnetization corresponding to magnetization generated by the90° pulse.

[0143] In FIG. 2D, a hyper-echo sequence precedes a conventionalsequence (in this case again a spin echo) to modify the contrastbehavior corresponding to the hyper-echo sequence, which may also bemodified for spin selection according to the principles described above.

[0144] The refocusing pulse flip angles α_(n) according to FIG. 3 aregenerally <180° and may be different from each other. Refocusing to acomplete echo amplitude may occur once (above) or several times (below).Application in imaging involves additional magnetic field gradientswhich are correspondingly switched (e.g. according to (D3)) in order toencode spatial information into the signal.

[0145] At the time of formation of the hyper-echo, a 90° pulse isapplied according to FIG. 3. During the multi-echo train, the transversemagnetization Mtr decays according to spin relaxation, z magnetizationMz recovers with T1. The relaxation curves are shown only schematically.The fully refocused transverse magnetization at the time of the hyperecho formation is transferred into z magnetization M_(DE). It is muchcloser to the equilibrium value M₀ than z magnetization M_(sat) withoutflipback (broken lines).

[0146] In FIGS. 5A through 5D, Rf, GS, GR and GP designate the radiofrequency pulses, and the slice selection, read and phase encodinggradients respectively. First, in FIG. 5A a number of m gradient echosare generated through m-fold repetition, wherein the flip angle α andphase Φ of the used pulses can be freely selected and are constant inthe most simple case (however, not necessarily preferred case).Subsequently, the refocusing pulse (in the simplest case a 180° pulse)is applied and finally the gradient echo sequence is repeated m times,wherein flip angle and phase of the used pulses are determined byequation [11]. The number of repetitions m can thereby be selectedfreely such that a complete data set required for image reconstructionis produced through single application or repeated application of thissequence.

[0147] When applied to z magnetization, the hyper-echo mechanism leadsto inversion. To realize a hyper-echo as transverse magnetization, thesequence can be preceded by an excitation pulse with a 90° flip angle inthe simplest case, as shown in FIG. 5B.

[0148]FIG. 5C shows a section from a gradient echo sequence comprisingseveral hyper echos, wherein also in this case, signal preparation canbe preceded by a 90° pulse like in FIG. 5B.

[0149]FIG. 5D shows a driven equilibrium sequence, wherein the formedhyper-echo is transferred by a corresponding flip back pulse in the zmagnetization.

[0150] The pulses used for hyper-echo formation in accordance with FIG.6 have excitation profiles which are shifted with respect to oneanother, such that the condition for forming a hyper-echo is met onlyfor spins whose resonance frequency is within the overlapping region(grey). Signals of spins which are detected only by part of the pulsesand for which the condition for hyper-echo formation is not met, aresuppressed. The dephasing intervals φ between the pulses are not shown.

[0151] The pulses in FIG. 7 show different excitation profiles (darkgrey). The hyper-echo conditions are met merely for individual spectralwindows (light grey).

[0152]FIG. 8A shows a sequence derived from the CPMG hyper-echo sequenceshown in FIG. 3 wherein an additional interval td was introduced beforethe central 180° pulse. For spins whose signal phase changes during td,the hyper-echo refocusing mechanism is no longer met.

[0153]FIG. 8B shows a sequence, wherein a motion-dependent change of thesignal phase is effected through an additional spin echo interval withsymmetrical magnetic field gradient G which also produces hyper-echoformation loss.

[0154]FIG. 8C shows that a motion-dependent change of the signal phaseand thus change of the amplitude of the hyper-echo can be effectedalready merely through corresponding magnetic field gradients alone inan otherwise unchanged hyper-echo sequence.

[0155] For coupled spins, a periodic phase change Φ of the two signalsof the doublet occurs due to J-coupling, whose spectrum S(ω) ischaracterized by a doublet as shown in FIG. 9. If a hyper-echo sequenceis applied to such a doublet, the phase Φ_(n) of each pulse is formallychanged by ±arcsin(t_(n)*J/2), wherein t_(n) is the time of the pulse.In general, the symmetry of the hyper-echo formation is disturbed andthe signals of coupled spins are not refocused. If the time of thecentral 180° pulse is 1/J, the symmetry remains unchanged. Thesedoublets are illustrated.

[0156]FIG. 10 finally shows a measuring sequence wherein at firstmagnetization is generated via hyper-echo formation (optionally with oneof the modifications described) and is subsequently read with anyread-out sequence.

[0157] Literature:

[0158] (D1) Hahn E L, Spin Echoes, Phys.Rev. 80:580-594 (1950)

[0159] (D2) Meiboom S, Gill D, Modified Spin-Echo Method for MeasuringNuclear Relaxation Times, Review of Scientific Instruments, 29:688-691(1958)

[0160] (D3) Hennig J, Multiecho Imaging Sequences with Low RefocusingFlip Angles, J.Magn.Reson., 78:397-407 (1988)

[0161] (D4) Le Roux P, Hinks R S, Stabilization of echo amplitudes inFSE sequences, Magn Reson Med. 30:183-90 (1993)

[0162] (D5) Alsop D C, The sensitivity of low flip angle RARE imaging,Magn Reson Med. 37:176-84 (1997)

[0163] (D6) Gullion T, Baker D E, Conradi M S., J.Magn.Reson. 89, 479(1990)

[0164] (D7) van Uijen C M, den Boef J H, Driven-equilibriumradiofrequency pulses in NMR imaging, Magn Reson Med. 1984Dec;1(4):502-7.

[0165] (D8) Hennig J, Thiel T, Speck O, Improved Sensitivity toOverlapping Multiplet Signals in in vivo Proton Spectroscopy Using aMultiecho Volume Selective (CPRESS-) Experiment, Magn Reson Med. 37:816-20 (1997)

[0166] (D9) Haase A, Snapshot FLASH MRI. Applications to T1, T2, andchemical-shift imaging, Magn Reson Med. 13:77-89 (1990)

[0167] (D10) Norris D G, Ultrafast low-angle RARE: U-FLARE, Magn ResonMed. 17: 539-542 (1991)

I claim:
 1. Method of NMR (=nuclear magnetic resonance) spectroscopy orNMR tomography, wherein a sequence of radio frequency pulses is appliedto a spin ensemble, characterized in that for at least 2n+1 consecutivepulses within the sequence, where n>1, with flip angles α₁ . . .α_(2n+1) and phases Φ₁ . . . Φ_(2n+1), of the pulses, between whichspins are respectively dephased by φ₁ . . . φ_(2n), the followingconditions are fulfilled: The central and (n+1)st pulse is used as arefocusing pulse with a preferred flip angle of 180°, Correspondingpulses placed symmetrically around the central and (n+1)st refocusingpulse have opposite phase and amplitude, consequently for the i-th pulsewith i between 1 and 2n+1 the following relations holdα_((n+1)−i)=−α_((n+1)+i) (the flip angle of the (n+1−i)th the pulse isequal to the opposite of the flip angle of the (n+1+i)th pulse) andΦ_((n+1)−i)=Φ_((n+1)−i) (the phase of the (n+1−i)th the pulse is equalto the opposite of the flip angle of the (n+1+i)th pulse) Dephasingintervals following the i-th pulse are-symmetrical around the centraland (n+1)st refocusing pulse according to the relation:φ_((n+1)−i)=φ_(n+i), (the dephasing interval after the (n+1−i)th pulseis identical to that after the (n+i)th pulse) such that at the end ofthe pulse sequence, the vector describing the initial magnetizationM_(A)(Mx,My,Mz) of the spin ensemble will appear to be rotated toM_(R)(−Mx,My,−Mz) by 180° around the axis of the radiofrequency field ofthe central refocusing pulse (=hyper-echo formation): M_(R)(−Mx,My,−Mz)=Rot _(y)(180°)* M _(A)(Mx,My,Mz)
 2. Method according toclaim 1, characterized in that the hyper-echo sequence is preceded by afurther rf-pulse used for excitation with a flip angle of optimally 90°,which leads to the formation of coherent magnetization M_(A) and whichwill accordingly then form M_(R) as fully coherent magnetization. 3.Method according to claim 2, characterized in that after the sequenceleading to hyper-echo formation a further radio frequency pulse isapplied the phase of which is orthogonal to the phase of M_(R) and theflip angle such that M_(R) is transformed into z magnetization , whereinthe time until adjustment of the thermal equilibrium of the excited spinsystem is shortened or when repeating the sequence with constantrecovering time, the intensity of the signals which contribute to thehyper echo, is increased.
 4. Method according to claim 2, characterizedin that after the sequence leading to hyper-echo formation a furtherradio frequency pulse is applied the phase of which is orthogonal to thephase of M_(R) and the flip angle such that M_(R) is transformed into −zmagnetization, wherein the time until adjustment of the thermalequilibrium of the excited spin system is prolonged or when repeatingthe sequence with constant recovering time, the intensity of the signalswhich contribute to the hyper echo, is shortened.
 5. Method according toclaim 1, characterized in that a pulse sequence is applied,corresponding to the hyper-echo formation, onto z magnetization suchthat at the end of the sequence, z magnetization is inverted.
 6. Methodaccording to claim 5, characterized in that a hyper-echo sequence isapplied to the spin system with pure z magnetization, whereinmagnetization is transferred into −z magnetization, followed by aninversion pulse, which again transfers the spin system into +zmagnetization, thereby reducing the time until adjustment of the thermalequilibrium of the excited spin system or increasing the intensity ofthe signals which contribute to the hyper-echo when the sequence isrepeated with constant recovering time.
 7. Method according to claim 1,characterized in that a pulse sequence is applied to transversemagnetization corresponding to hyper-echo formation such that transversemagnetization is refocused at the end of the sequence.
 8. Methodaccording to claim 1, characterized in that the measuring sequenceconsists of an excitation pulse with subsequent multiple refocusing inthe sense of a multi-echo sequence, such that hyper-echo formation iscarried out once or several times during the multi-echo sequence therebyforming one or more hyper-echos during each multi-echo train.
 9. Methodaccording to claim 1, characterized in that the symmetry required forhyper-echo formation is disturbed through a modulation step E such thatmerely spins whose phase is not disturbed by the modulation stepcontribute to hyper-echo formation whereas spins for which themodulation step effects a phase change, form a correspondinglyattenuated hyper-echo.
 10. Method according to claim 1, characterized inthat spin selection is carried out such that the phase of signals ofspins with J-coupling, zero and multiple-quantum coherences differs fromthe phase of spins in uncoupled signals such that a hyper-echo is formedonly for uncoupled spins.
 11. Method according to claim 1, characterizedin that a spin selection is carried out such that the phase of the radiofrequency pulses follows the phase development of spins with J-coupling,zero or multiple-quantum coherences etc. such that a hyper-echo isformed only for those spins for which the conditions for hyper-echoformation are met.
 12. Method according to claim 1, characterized inthat hyper-echo formation is carried out on the basis of an imagingsequence, preferably RARE, GRASE, Echo Planar Imaging, FLASH, or SpiralImaging.
 13. Method according to claim 1, characterized in that ahyper-echo is formed after excitation of the spin system andsubsequently the signal of the hyper echo is read.
 14. Method accordingto claim 13, characterized in that an imaging sequence, preferably RARE,Echo Planar Imaging, Snapshot-FLASH or Spiral Imaging is used forreading out a signal.
 15. Method according to claim 1, characterized inthat a measuring sequence is applied to several nuclei with differentgyromagnetic relationship, wherein the partial sequence acting on atleast one nucleus, effects hyper-echo formation.